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A Dynamic SIqIRV Mathematical model with Non-linear Force of Isolation, Infection and Cure 具有非线性隔离力、感染力和治愈力的动态SIqIRV数学模型
Nonautonomous Dynamical Systems Pub Date : 2022-01-01 DOI: 10.1515/msds-2022-0145
G. Chatzarakis, S. Dickson, S. Padmasekaran
{"title":"A Dynamic SIqIRV Mathematical model with Non-linear Force of Isolation, Infection and Cure","authors":"G. Chatzarakis, S. Dickson, S. Padmasekaran","doi":"10.1515/msds-2022-0145","DOIUrl":"https://doi.org/10.1515/msds-2022-0145","url":null,"abstract":"Abstract The Susceptible-Isolated-Infected-Recovered-Vaccinated (SIqIRV) deterministic model is examined in this paper. This model considers a nonlinear force of quarantine, infection and care, where vaccinated individuals lose their immunity after a period of time and become susceptible to infection. Isolation is the main key to bringforth the SIqIRV model. The fundamentals of reproduction number calculated using this model is an outbreak threshold that decides whether or not a disease can spread. The infection free steady state solutions are locally and globally found to be asymptotically stable when R0 < 1. Infection persistent steady state solutions are also found to be locally asymptotically stable when R0 > 1. At the end, computational simulations were run to confirm and support our theoretical findings.","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","volume":"9 1","pages":"56 - 67"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41949298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
New Development Theory on Measure Pseudo – Asymptotically Omega Periodic Functions 测度伪渐近Omega周期函数的新发展理论
Nonautonomous Dynamical Systems Pub Date : 2022-01-01 DOI: 10.1515/msds-2022-0144
E. A. Dads, L. Lhachimi
{"title":"New Development Theory on Measure Pseudo – Asymptotically Omega Periodic Functions","authors":"E. A. Dads, L. Lhachimi","doi":"10.1515/msds-2022-0144","DOIUrl":"https://doi.org/10.1515/msds-2022-0144","url":null,"abstract":"Abstract The main goal of the paper concerns two parts, in the ˝rst one, we extend some results from Blot et al [5] under general hypothesis on the measure, in the second part, we introduce a new class of functions, which we call measure pseudo 𝒮 - asymptotically omega periodic functions. The obtained results is the extension of those established recently in the literature. Then we establish many interesting results on those functions, namely their characterization, we give also several properties of those class of functions as composition results, the invariance by translation, and the convolution product. All sections are illustrated by examples or counter examples.","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","volume":"9 1","pages":"21 - 36"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46489429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Existence and Stability Results of Stochastic Differential Equations with Non-instantaneous Impulse and Poisson jumps 具有非瞬时脉冲和泊松跳的随机微分方程的存在性和稳定性结果
Nonautonomous Dynamical Systems Pub Date : 2022-01-01 DOI: 10.1515/msds-2022-0159
S. Varshini, K. Banupriya, K. Ramkumar, K. Ravikumar
{"title":"Existence and Stability Results of Stochastic Differential Equations with Non-instantaneous Impulse and Poisson jumps","authors":"S. Varshini, K. Banupriya, K. Ramkumar, K. Ravikumar","doi":"10.1515/msds-2022-0159","DOIUrl":"https://doi.org/10.1515/msds-2022-0159","url":null,"abstract":"Abstract This paper focuses on a new class of non-instantaneous impulsive stochastic differential equations generated by mixed fractional Brownian motion with poisson jump in real separable Hilbert space. A set of sufficient conditions are generated based on the stochastic analysis technique, analytic semigroup theory of linear operators, fractional power of operators, and fixed point theory to obtain existence and uniqueness results of mild solutions for the considered system. Furthermore, the asymptotic behaviour of the system is investigated. Finally, an example is proposed to validate the obtained results.","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","volume":"9 1","pages":"256 - 271"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41723325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Existence and Stability Results for Coupled Fractional Dynamic System with Impulses over Non-uniform Time Domains 非均匀时域上脉冲耦合分数阶动力系统的存在性和稳定性结果
Nonautonomous Dynamical Systems Pub Date : 2022-01-01 DOI: 10.1515/msds-2022-0146
Vipin Kumar, Muslim Malik
{"title":"Existence and Stability Results for Coupled Fractional Dynamic System with Impulses over Non-uniform Time Domains","authors":"Vipin Kumar, Muslim Malik","doi":"10.1515/msds-2022-0146","DOIUrl":"https://doi.org/10.1515/msds-2022-0146","url":null,"abstract":"Abstract In this manuscript, we examine the existence, uniqueness and stability results for a coupled fractional dynamical system with impulsive and initial-boundary (IB) conditions on non-uniform time domains by implying the theory of time scales. Firstly, we find the solution of the consider problem, then we examine the existence and stability results. Mainly, we use the Banach and Leray-Schauder’s alternative type fixed point theorems to establish the main results. At last, we present an example to illustrate the utilization of these analytical outcomes.","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","volume":"9 1","pages":"37 - 55"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43085143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Oscillation and Property B for Semi-Canonical Third-Order Advanced Difference Equations 半正则三阶高级差分方程的振动性和性质B
Nonautonomous Dynamical Systems Pub Date : 2022-01-01 DOI: 10.1515/msds-2021-0142
G. Chatzarakis, R. Srinivasan, E. Thandapani
{"title":"Oscillation and Property B for Semi-Canonical Third-Order Advanced Difference Equations","authors":"G. Chatzarakis, R. Srinivasan, E. Thandapani","doi":"10.1515/msds-2021-0142","DOIUrl":"https://doi.org/10.1515/msds-2021-0142","url":null,"abstract":"Abstract In this paper, we present sufficient conditions for the third-order nonlinear advanced difference equations of the form Δ(a(n))Δ(b(n)Δy((n)))=p(n)f(y(σ(n))) Delta left( {aleft( n right)} right)Delta left( {bleft( n right)Delta yleft( {left( n right)} right)} right) = pleft( n right)fleft( {yleft( {sigma left( n right)} right)} right) to have property B or to be oscillatory. These conditions are based on monotonic properties and estimates of nonoscillatory solutions of corresponding canonical type equations. The obtained results extended and improve known results mentioned in the literature.","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","volume":"9 1","pages":"11 - 20"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45725797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Necessary and Sufficient Conditions for Oscillation of Nonlinear Neutral Difference Systems of dim-2 dim-2非线性中立型差分系统振动的充分必要条件
Nonautonomous Dynamical Systems Pub Date : 2022-01-01 DOI: 10.1515/msds-2022-0148
A. Tripathy, Sunita Das
{"title":"Necessary and Sufficient Conditions for Oscillation of Nonlinear Neutral Difference Systems of dim-2","authors":"A. Tripathy, Sunita Das","doi":"10.1515/msds-2022-0148","DOIUrl":"https://doi.org/10.1515/msds-2022-0148","url":null,"abstract":"Abstract This work is concerned about the necessary and sufficient conditions for oscillation of solutions of 2-dimensional nonlinear neutral delay difference systems of the form: Δ[ x(n)+p(n)x(n−m)y(n)+p(n)y(n−m) ]=[ a(n)b(n)c(n)d(n) ]  [ f(x(n−α))g(y(n−β)) ], Delta left[ {matrix{ {xleft( n right) + pleft( n right)xleft( {n - m} right)} hfill cr {yleft( n right) + pleft( n right)yleft( {n - m} right)} hfill cr } } right] = left[ {matrix{ {aleft( n right)} hfill & {bleft( n right)} hfill cr {cleft( n right)} hfill & {dleft( n right)} hfill cr } } right],,left[ {matrix{ {fleft( {xleft( {n - alpha } right)} right)} hfill cr {gleft( {yleft( {n - beta } right)} right)} hfill cr } } right], where m > 0, α ≥ 0, β ≥ 0 are integers, a(n), b(n), c(n), d(n), p(n) are real sequences and f, g ∈ 𝒞(ℝ, ℝ).","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","volume":"9 1","pages":"91 - 102"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46598983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stepanov type µ-pseudo almost automorphic mild solutions of semilinear fractional integrodifferential equations 半线性分数阶积分微分方程的Stepanov型微-伪几乎自同构温和解
Nonautonomous Dynamical Systems Pub Date : 2022-01-01 DOI: 10.1515/msds-2022-0152
J. Sousa, G. N’Guérékata
{"title":"Stepanov type µ-pseudo almost automorphic mild solutions of semilinear fractional integrodifferential equations","authors":"J. Sousa, G. N’Guérékata","doi":"10.1515/msds-2022-0152","DOIUrl":"https://doi.org/10.1515/msds-2022-0152","url":null,"abstract":"Abstract In this paper, using necessary and sufficient conditions, the new concept of Stepanov µ-pseudo almost automorphic functions and ergodicity results, we investigate the existence of mild bounded solutions for a class of fractional integro-differential equations in the sense of the Weyl fractional derivative in a Banach space.","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","volume":"9 1","pages":"145 - 162"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47318786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
On the existence of global weak solutions of a 2D sediment transport model 二维输沙模式整体弱解的存在性
Nonautonomous Dynamical Systems Pub Date : 2022-01-01 DOI: 10.1515/msds-2022-0153
Yacouba Zongo, Brahima Roamba, Boulaye Yira, Jean De Dieu Zabsonré
{"title":"On the existence of global weak solutions of a 2D sediment transport model","authors":"Yacouba Zongo, Brahima Roamba, Boulaye Yira, Jean De Dieu Zabsonré","doi":"10.1515/msds-2022-0153","DOIUrl":"https://doi.org/10.1515/msds-2022-0153","url":null,"abstract":"Abstract In the abstract, homogenize the references as follows: In this paper,we study the existence of global weak solutions of a two dimensionnal model. The model is inspired by the one studied in [Math. Models Methods Appl. Sci. 19 (2009), 477-499]. Our model is a particular case of the two-dimensionnal sediment transport model derived in [Mathematical Modelling and Numerical Analysis 51 (2017), 115-145]. The main contribution of this article is to extend the results obtained 10 in [C. R. Math. Acad. Sci. Paris, 344 (2007), 443-446; Math. Models Methods Appl. Sci. 19 (2009), 477-499] by showing the existence of global weak solution of a sediment transport model without assuming the data to be small enough, following the ideas proposed in [Inv. Math.206 (2016), 935-974].","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","volume":"9 1","pages":"182 - 204"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43890152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Local existence and blowing up phenomena for a class of non-autonomous partial functional differential equations with infinite delay 一类具有无限时滞的非自治偏泛函微分方程的局部存在性和爆破现象
Nonautonomous Dynamical Systems Pub Date : 2022-01-01 DOI: 10.1515/msds-2022-0156
M. Diop, K. Ezzinbi, B. A. Kyelem
{"title":"Local existence and blowing up phenomena for a class of non-autonomous partial functional differential equations with infinite delay","authors":"M. Diop, K. Ezzinbi, B. A. Kyelem","doi":"10.1515/msds-2022-0156","DOIUrl":"https://doi.org/10.1515/msds-2022-0156","url":null,"abstract":"Abstract In this work, we study a class of abstract non-autonomous partial functional differential equations with infinite delay. Our main results concern the local existence of the mild solution which can blow up at the finite time. The unbounded operators associated to the non-autonomous system are assumed to be stable family which generates C0-semigroups while the nonlinear part is supposed to be continuous. Under Lipschitz condition on the nonlinear term of the equation, we prove the existence and uniqueness of the mild solution. For illustration, we provide an example for some reaction-diffusion non-autonomous partial functional differential equations involving infinite delay.","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","volume":"9 1","pages":"237 - 255"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44678099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability Analysis of B.1.1.529 SARS-Cov-2 Omicron Variant Mathematical Model: The Impacts Of Quarantine And Vaccination B.1.1.529 SARS-Cov-2组元变异数学模型的稳定性分析:检疫和疫苗接种的影响
Nonautonomous Dynamical Systems Pub Date : 2022-01-01 DOI: 10.1515/msds-2022-0158
S. Dickson, S. Padmasekaran, G. Chatzarakis
{"title":"Stability Analysis of B.1.1.529 SARS-Cov-2 Omicron Variant Mathematical Model: The Impacts Of Quarantine And Vaccination","authors":"S. Dickson, S. Padmasekaran, G. Chatzarakis","doi":"10.1515/msds-2022-0158","DOIUrl":"https://doi.org/10.1515/msds-2022-0158","url":null,"abstract":"Abstract In this study, an epidemic mathematical model for Omicron, denoted as B.1.1.529 SARS-Cov-2 Variant, is constructed. Covid-19 vaccines are considered here to ensure the host population’s safety across the model. The fundamentals of positivity and boundedness in this model have been investigated and validated. The reproduction number was calculated to determine whether or not the disease would spread further in Tamilnadu. Infection-free steady-state solutions that exist are asymptotically stable locally when R0 < 1 and globally when R0 > 1. Also Infection-present steady-state solutions that are locally stable are discovered when R0 < 1. Finally, the current Omicron variant pandemic data from Tamilnadu, India, is validated.","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","volume":"9 1","pages":"290 - 306"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48499270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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